The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.

1.
Agrawal
S. K.
, and
Roth
B.
,
1992
, “
Statics of In-Parallel Manipulator Systems
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
114
, pp.
564
568
.
2.
Arai, T., Cleary, K., Nakamura, T., Adachi, H., and Homma, K., 1990, “Design, Analysis and Construction of a Prototype Parallel Link Manipulator,” Proc. of the 1990 IEEE Int. Workshop on Intelligent Robots and Systems. IROS’90, pp. 205–212.
3.
Baron, L., and Angeles, J., 1994, “The Decoupling of the Direct Kinematics of Parallel Manipulators Using Redundant Sensors,” Proc. of the 1994 IEEE Int. Conf. on Robotics and Automation, San Diego, CA, May 8–13, pp. 974–979.
4.
Baron, L., and Angeles, J., 1995, “A Linear Algebraic Solution of the Direct Kinematics of Parallel Manipulators Using a Camera,” Proc. of the Ninth World Congress on the Theory of Machines and Mechanisms, Milano, Italy, Aug. 29–Sept. 2, pp. 1925–1929.
5.
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North-Holland Publishing Co., Amsterdam.
6.
Cheng
H.
, and
Gupta
K. C.
,
1989
, “
An Historical Note on Finite Rotations
,”
ASME Journal of Applied Mechanics
, Vol.
56
, pp.
139
145
.
7.
Cheock
K. C.
,
Overholt
J. L.
, and
Beck
R. R.
,
1993
, “
Exact Methods for Determining the Kinematics of a Stewart Platform Using Additional Displacement Sensors
,”
Journal of Robotic Systems
, Vol.
10
, No.
5
, pp.
689
707
.
8.
Fichter
E. F.
,
1986
, “
A Stewart Platform-Based Manipulator: General Theory and Practical Construction
,”
The Int. Jou. of Robotics Research
, Vol.
5
, No.
2
, pp.
157
182
.
9.
Han, K., Chung, W., and Youm, Y., 1995, “Local Structurization for the Forward Kinematics of Parallel Manipulators Using Extra Sensor Data,” Proc. of the IEEE Int. Conference on Robotics and Automation, Nagoja, Japan, May 25–27, pp. 514–520.
10.
Husty
M.
,
1996
, “
An Algorithm for Solving the Direct Kinematic of Stewart-Gough-Type Platforms
,”
Mechanism and Machine Theory
, Vol.
31
, No.
4
, pp.
365
380
.
11.
Innocenti, C., and Parenti Castelli, V., 1992, “Singularity-Free Evolution from One Configuration to Another in Serial and Parallel Manipulators,” Proc. of the 22nd ASME Mechanisms Conference, Phoenix, AZ, Sept. 13–16, DE-Vol. 45, pp. 553–560; to be published in the ASME JOURNAL OF MECHANICAL DESIGN.
12.
Jin, Y., 1994, “Exact Solution for the Forward Kinematics of the General Stewart Platform Using Two Additional Displacement Sensors,” Proc. of the 23rd ASME Mechanisms Conference, DE-Vol. 72, Minneapolis, MN, Sept. 11–14, pp. 491–495.
13.
Kumar
V.
,
1992
, “
Instantaneous Kinematics of Parallel-Chain Robotic Mechanisms
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
114
, No.
3
, pp.
349
358
.
14.
Lazard, D., 1993, “On the Representation of Rigid-Body Motions and its Applications to Generalized Platform Manipulators,” Computational Kinematics, J. Angeles, G. Hommel, and P. Kovacs, eds., Kluwer Academic Publishers, Dordrecht, pp. 175–181.
15.
Masory, O., and Wang, J., 1992, “Workspace Evaluation of Stewart Platforms,” Proc. of the 22nd. Biennial ASME Mechanisms Conference, DE-Vol. 45, Scottsdale, AZ, Sept. 13–16, pp. 337–346.
16.
Merlet, J. P., 1993, “Closed-Form Resolution of the Direct Kinematics of Parallel Manipulators Using Extra Sensors Data,” IEEE Int. Conf. on Robotics and Automation, Atlanta, pp. 200–204.
17.
Parenti Castelli, V., and Di Gregorio, R., 1995, “Determination of the Actual Configuration of the General Stewart Platform Using Only One Additional Displacement Sensor,” ASME Paper 95-WA/AD-6.
18.
Raghavan
M.
,
1993
, “
The Stewart Platform of General Geometry has 40 Configurations
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
115
, No.
2
, pp.
277
282
.
19.
Raghavan
M.
, and
Roth
B.
,
1995
, “
Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot, Manipulators
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
117
, Special 50th Anniversary Design Issue, pp.
71
79
.
20.
Shi, X., and Fenton, R. G., 1991, “Forward Kinematic Solution of a General 6 DOF Stewart Platform Based on Three Point Position Data,” Proc. of the Eighth World Congress on the Theory of Machines and Mechanisms, Prague, Czechoslovakia, Aug. 26–31, pp. 1015–1018.
21.
Stoughton, R., and Arai, T., 1991, “Optimal Sensor Placement for Forward Kinematics Evaluation of a 6-DOF Parallel Link Manipulator,” Proc. of the IEEE/RSJ Int. Workshop on Intelligent Robots and Systems, IROS’91, Nov. 3–5, pp. 785–790.
22.
Tancredi, L., Teillaud, M., and Merlet, J. P., 1995, “Extra Sensors for Solving the Forward Kinematics Problem of Parallel Manipulators,” Proc. of the Ninth World Congress on the Theory of Machines and Mechanisms, Milano, Italy, Aug. 29–Sept. 2, pp. 2122–2126.
23.
Waldron, K. J., and Hunt, K. H., 1987, “Series-Parallel Dualities in Actively Coordinated Mechanisms,” Proc. of the Fourth Int. Symp. on Robotics Research, Santa Cruz, CA, Aug. 9–14, pp. 233–239.
24.
Wampler
C.
,
1996
, “
Forward Displacement Analysis of General Six-in-Parallel SPS (Stewart) Platform Manipulators using Soma Coordinates
,”
Mechanism and Machine Theory
, Vol.
31
, No.
3
, pp.
331
337
.
25.
Zanganeh
K. E.
, and
Angeles
J.
,
1995
, “
Real-Time Direct Kinematics of General Six-Degree-of-Freedom Parallel Manipulators with Minimum-Sensor Data
,”
Journal of Robotic Systems
, Vol.
12
, No.
12
, pp.
833
844
.
This content is only available via PDF.
You do not currently have access to this content.